Disagreement and Belief Dependence: Showing When and How the Numbers Count
Word Count: 2999
While taking a logic exam, you encounter a problem you do not know how to do. So you decide
to cheat. Your friends Alice, Bob, and Carol are seated close by, and you know that they are all
quite good at logic – about equally good, in fact. You peek at their answers and find that they did
not all agree: Alice obtained ~p; Bob and Carol obtained p. What do you do?
Other things the same, you should
go with p. You have two reliable sources against one. But
suppose that you saw Carol copy off of Bob. With this information, it seems clear that you do not
to favor p. Even though the case can still be described as ‘two against one,’ Carol's
opinion is dependent on Bob's, in some important sense. And, for this reason, it seems not to
“count” (i.e. it seems not to provide additional support for p beyond that provided by Bob's
opinion). To accommodate cases like this, we might offer the following general principle:
Belief Dependence: When one opinion is totally dependent on another, the dependent opinion does
not confer any additional support for the jointly held proposition.
Precedent for such a principle is easy to find. Here is Adam Elga:1
[A]n additional outside opinion should move one only to the extent that one counts it as independent
from opinions one has already taken into account.
Elga regards this claim as “completely uncontroversial” and suggests that “every sensible view
on disagreement should accommodate it.” Tom Kelly, writing from the other side of the
disagreement debate, shares Elga’s outlook.2 But despite its widespread appeal, Jennifer Lackey
(2013) argues, persuasively, that Belief Dependence cannot be generally true:3
See Elga (2010, p. 177).
See Kelly (2010, p. 148).
See Lackey (p. 245).